Question

There is/are _________________ between two given rational numbers.

• A. one and only one rational number
• B. only ten rational numbers
• C. infinitely many rational numbers
• D. only two rational numbers

Answer 1

The correct option is C infinitely many rational numbers

There will be countless rational numbers between any two rational numbers.

For example, rational numbers between $\frac{-1}{10}$ and $\frac{3}{10}$.

$\frac{0}{10}$, $\frac{1}{10}$, $\frac{2}{10}$ are the obvious rational numbers between them.

But $\frac{-1}{10}$ can be written as $\frac{-10000}{100000}$ and $\frac{3}{10}$ = $\frac{30000}{100000}$

So, rational number between $\frac{-1}{10}$ and $\frac{3}{10}$ are $\frac{-9999}{100000}$, $\frac{-9998}{100000}$ ,…..$\frac{29998}{100000}$, $\frac{29999}{100000}$
Thus, we can find infinite rational numbers between any two rational numbers.